Want a safe, secure web browser? Try Firefox… it will run on most computers and it's not filled with security holes and bugs like some other browsers. It's important to run a secure web browser because security flaws can make it relatively easy for a malicious web site to do something bad to your computer, like give you a virus or get unauthorized access to your files. Whichever browser you choose, be sure to check its website and update it regularly so you have all of the latest security fixes and cool new features. You can get Firefox here:

http://www.getfirefox.com

For a quick read on browser market share and the state of browser security, check out this article from The Register:

http://www.theregister.co.uk/2005/04/28/_ie_firefox/